(1) \( x^{2}+32 x+256=0 \)

Did you know that the equation \( x^{2}+32x+256=0 \) can actually be solved using a simple technique called factoring? In this case, you can rewrite it as \( (x+16)^2=0 \). This means that \( x+16=0 \), leading you to the elegant solution of \( x=-16 \). It’s a neat little trick that helps you avoid complicated steps! Now, if you're diving into quadratic equations, remember that the discriminant (the part under the square root in the quadratic formula) can hint at the nature of the solutions. Here, \( b^2 - 4ac = 32^2 - 4(1)(256) = 0 \) tells us there’s exactly one solution since it equals zero. Keep an eye on the discriminant; it can save you time and effort unraveling the mysteries of quadratics!